Abstract

Lightning events can cause fast polarization rotations and phase changes in optical transmission fibers due to strong electrical currents and magnetic fields. Whereas these are unlikely to affect legacy transmission systems with direct detection, different mechanisms have to be considered in systems with local oscillator based coherent receivers and digital signal processing. A theoretical analysis reveals that lightning events can result in polarization rotations with speeds as fast as a few hundred kRad/s. We discuss possible mechanisms how such lightning events can affect coherent receivers with digital signal processing. In experimental investigations with a high current pulse generator and transponder prototypes, we observed post FEC errors after polarization rotation events which can be expected from lightning strikes.

© 2016 Optical Society of America

1. Introduction

Lightning is an impressive weather phenomenon. The involved high voltages, strong electrical currents and large amounts of energy can cause considerable damage. Whereas the impact of strong electrical fields corresponding to the high voltages on silica fiber based optical transmission can usually be neglected due to the very weak Kerr effect in silica glass, magnetic fields generated by strong electrical currents potentially result in significant polarization rotations due to the Faraday effect. This raises the question, whether lightning events can have an impact on state of the art long haul transmission equipment with local oscillator based coherent detection and digital signal processing.

Fast polarization changes have not affected the early generations of optical transmission systems. These systems were based on symbol rates of 10 GBaud or below, binary intensity modulation, and direct detection and therefore feature a phase and polarization insensitive operation. Since then, several concepts have been studied which introduce polarization sensitivity. In the years around 2000, polarization multiplexing (PolMUX) was investigated to double the capacity of channels in wavelength division multiplexing (WDM) transmission systems [1]. An optical polarization controller in front of a polarization beam splitter had to be adjusted appropriately in order to separate the two orthogonal polarization channels at the output of the link.

The transition of channel bitrates from 10 Gbit/s to 40 Gbit/s resulted in a need for polarization mode dispersion (PMD) compensation. Due to this effect, many installed fibers did not support transmission of 40 Gbit/s signals over distances of several 100 km with the modulation formats of the first generations of commercial transponders, namely duobinary and differential phase shift keying (DPSK) with symbol rates of 40 GBaud. Optical PMD compensation was studied as an approach to improve the PMD tolerance of these systems. Optical polarization controllers were combined with differential group delay (DGD) elements in order to approximate the inverse PMD transfer function of the link. As in the PolMUX case, the polarization controllers have to be adjusted appropriately and have to be able to track potential polarization changes occurring along the link over time.

In order to design the response time of the controllers appropriately, information was needed about the speed of polarization changes which have to be expected in installed links. Several studies were carried out in order to identify mechanisms which potentially generate fast polarization changes and to determine the magnitude, speed, and frequency of occurrence of polarization rotations which have to be expected [2–4]. Realizing response times of the optical polarization controllers suitable to follow the sub millisecond polarization rotations observed in the studies was challenging but feasible.

The development of optical PMD compensators was terminated abruptly around the year 2005 due to the emergence of a new approach. Local oscillator based coherent detection in combination with digital signal processing (DSP) enabled the compensation or mitigation of signal distortions resulting from linear effects such as chromatic dispersion (CD) and PMD [5]. The polarization dependence of the mixing of the local oscillator signal with the received signal in the photo diodes also results in a need for adaptive polarization control. But instead of realizing this polarization control in the optical domain by optical polarization controllers in front of the photo diode as in the case of PolMUX or optical PMD compensation, a different approach was adopted.

Polarization diversity, i. e. the separate detection of two randomly chosen orthogonal polarizations of the receiver input signal, enables to implement the polarization control in the digital domain [5,6]. A digitally implemented butterfly filter structure acting as a multiple input / multiple output (MIMO) equalizer is usually deployed to undo polarization rotations occurring along the link and to restore two orthogonal polarization components of the transmitted signal. As the polarization diversity of the local oscillator based coherent detection and the butterfly equalizer are required to enable the receiver to accept arbitrary input polarizations, it suggests itself to use them also to implement polarization multiplexing for the doubling of the capacity per WDM channel.

Due to the implementation of polarization control in the digital domain, response times well beyond one millisecond can be realized easily. These response times close to 1 µs seem to be sufficient to follow polarization rotations resulting from temperature fluctuation or mechanical vibrations. However, care should be taken due to the change in the detection concept. Contrary to the phase insensitivity of direct detection, local oscillator based coherent detection is sensitive to fluctuations of the signal phase.

Lightning events have been studied as a potential source of polarization transients in optical aerial cables [7,8]. Optical fibers installed in overhead ground wires of electrical power transmission lines are exposed to effects resulting from strong electrical currents, especially if lightning hits the ground wire. However, polarization transients have also been observed, if the lightning event occurred at a certain distance from the electrical power transmission line [7]. Even in the field trial on a link with optical fiber cables buried in the ground, one recorded trace seems to have resulted from a lightning event near the cable according to the observable signature [4].

The conclusion in [8] was that fast polarization effects resulting from lightning and impulse current may induce penalties in optical transmission systems with direct detection, but these penalties are negligible. We suggest that it is worth studying, whether the same conclusion can be drawn for systems with local oscillator based coherent detection and digital signal processing. To our best knowledge, this is the first report on investigations of the impact of polarization rotations caused by lightning events on this receiver type. A theoretical analysis and experimental investigations indicate that polarization transients caused by lightning events result in very demanding requirements on response times of coherent receivers which may not be met by all existing implementations.

2. Theoretical analysis of polarization transients due to magnetic fields

2.1 Polarization rotations due to the Faraday effect

Lightning events near cabled fibers can alter the polarization of transmitted optical signals due to the Faraday effect. Figure 1 shows the configuration which is considered to calculate the magnitude of resulting polarization rotations. The lightning current I is assumed to flow through the origin of the coordinate system in the direction of the x-axis. A cable with optical transmission fibers is located at a distance d from the origin pointing parallel to the z axis.

 

Fig. 1 Sketch of the configuration which is considered to calculate the impact of lightning current on optical fiber transmission.

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The electrical current along the x-axis results in concentric magnetic field lines in the y-z-plane. The magnitude of the magnetic field vector H at a distance r can be calculated by using the respective Maxwell equation or Ampère’s law in integral form:

I=l|H|dl.
Due to the rotational symmetry of the field lines, this equation can be transformed into the simpler expression:
|H(r)|=I2πr.
The distance r from the x-axis can be calculated from the y- and the z-coordinate of a given location:
r=y2+z2.
Equation (2) combined with Eq. (3) enable to calculate the magnitude of the magnetic field vector inside the optical transmission fiber as a function of the z-coordinate:
|H(z)|=I2πd2+z2,
where the placement of the fiber at y = d has been taken into account.

The Faraday effect results in a rotation of the polarization of an electromagnetic wave caused by a magnetic field oriented in the direction of the wave propagation. Consequently, only the z-component of the magnetic field vector in the fiber contributes to the Faraday effect. As the magnetic field vector is oriented at an angle α with respect to the fiber axis, its z-component exhibits the angular dependence:

Hz=|H|cos(α).
The cosine function of the angle α can also be expressed by the ratio of the distance d of the fiber from the origin of the coordinate system and the spacing r between a given location along the fiber and the origin:
cos(α)=dr=dd2+z2.
Combining Eqs. (4), (5), and (6) enables to express the z-component of the magnetic field vector at any given location along the fiber as a function of the z-coordinate:
Hz(z)=dI2π(d2+z2).
The incremental polarization rotation of the propagating electromagnetic wave, i. e. the rotation of the electric field vector by the angle per incremental length dz is proportional to the z-component of the magnetic flux density Bz:
dθdz=VBz
with the proportionality factor V which is called Verdet constant. The relative permeability µr of silica glass is very close to one, so the z-component of the magnetic flux density can be approximated as:
Bz(z)=μ0Hz(z)=μ0dI2π(d2+z2),
where µ0 denotes the permeability in free space. The angle of the total polarization rotation can be calculated by integrating the product of the Verdet constant and the z-component of the magnetic flux density over the entire length of the fiber and taking the symmetry of the configuration into account:
θ=VBzdz=2V0Bzdz=Vμ0dIπ01d2+z2dz.
By solving the integral, Eq. (10) can be transformed into the surprisingly simple equation:
θ=Vμ0I2.
According to this equation, the total polarization rotation of the electromagnetic wave propagating in the fiber only depends on the strength of the lightning current I and some constants. It is interesting to note that it does not depend on the distance d between the lightning current and the fiber.

In order to facilitate the interpretation of this result, it is helpful to define an effective length leff. This length is chosen to obtain the same polarization rotation in a fiber where the magnetic flux density is constant along this length as in a fiber where the flux density monotonically decreases from a maximum value to zero. For the value of the constant flux density, we select the maximum value occurring in the fiber with varying flux density. In the configuration depicted in Fig. 1, this maximum value occurs at z = 0. According to this definition of the effective length, the angle of the total polarization rotation θS in the relevant fiber section from the point closest to the current to locations very far away from it can be calculated as:

θS=Vμ0Hz(z=0)leff=0Vμ0Hz(z)dz.
By considering Eq. (7), we get:
Hz(z=0)=I2πd.
Inserting this equation and Eq. (7) into Eq. (12) and solving the integral leads to the following expression for the effective length:
leff=dπ2.
The angle of the polarization rotation θS experienced by the optical signal propagating through the fiber section with z ≥ 0 can hence be calculated as:
θS=Vμ0Hz(z=0)leff=Vμ0I2πddπ2=14Vμ0I.
According to the symmetry of the configuration depicted in Fig. 1, the polarization rotation angle θS in the fiber section with z ≥ 0 corresponds to half of the entire polarization rotation, which can be verified by comparing Eq. (15) with Eq. (11).

The effective length also lends itself to a geometric interpretation. In the configuration depicted in Fig. 1, the fiber section responsible for the polarization rotation starts at the point with minimum distance from the lightning current and maximum field strength at z = 0 and runs to z → ∞ in a straight line. If the fiber was following a section of a circle in the y-z-plane which is centered on the lightning current, the magnetic field strength and the flux density would remain constant along such a section of the fiber. This configuration is depicted in Fig. 2. In this case, the fiber follows a magnetic field line and the entire magnetic field strength contributes to the Faraday effect in a section of the circle defined by the angle δ.

 

Fig. 2 Optical fiber following a segment of a circle around the lightning current.

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The length of the fiber segment following the field line can be calculated as:

lF=2πdδ2π=dδ
with the angle δ in rad. The angle of the polarization rotation experienced by an optical signal propagating through the fiber segment can be calculated as:
θF=Vμ0Hz(z=0)lF=Vμ0Iδ2π.
If the angle is chosen as δ = π/2 rad, the polarization rotation angle assumes the same value as the one in Eq. (15). Consequently, the effective length defined by Eq. (12) can also be interpreted as the length of a fiber section following a field line according to the configuration in Fig. 2 for a quarter of a circle. The entire polarization rotation in the straight line fiber configuration depicted in Fig. 1 would also be achieved by a fiber following a semicircle.

As in the configuration depicted in Fig. 1, the polarization rotation angle experienced by the optical signal in the configuration depicted in Fig. 2 does not depend on the spacing d between the lightning current and the fiber, which in this case corresponds to the radius of the circle. The increasing length of the fiber section with increasing spacing or radius is exactly compensated by the reduction of the magnetic field strength. This observation seems to imply that lightning events at a distance of several hundred kilometers will induce the same polarization rotation as events occurring nearby in case of long haul optical fiber links extending over a few thousand kilometers. This would result in a large number of polarization transients during seasons with high thunderstorm activity.

Fortunately, all expressions for the polarization rotation angle discussed so far are only valid, if an important requirement is met. The magnetic field strength must remain constant during the propagation of the optical signal through the relevant fiber section. Due to the usually short duration of lightning events, this requirement is only met for lightning events in the vicinity of the fiber. The electrical current flowing in the discharge arc of a typical lightning event exhibits a rise time around 1 µs and a total duration around 20 µs with a slow decay [9]. Due to the group refractive index around ngr = 1.47 of silica glass at a wavelength around 1550 nm, the optical signal travels a distance ΔzOS of approx. 200 m per µs. In order to achieve a similar polarization rotation as in the case with static magnetic fields, the optical signal has to travel at least twice the effective length of the configuration depicted in Fig. 1 during the transient event with a duration τ:

ΔzOS=c0ngrτ>2leff,
where c0 denotes the speed of light in free space. With these restrictions and Eq. (14), an upper limit for the spacing between the lightning current and the transmission fiber can be calculated:
dmax<c0τπngr,
With a peak current lasting for τ = 10 µs, the lightning event has to occur closer than 650 m away from the fiber to generate the full polarization rotation.

These distance considerations can be used to calculate an average rate of polarization transients. In many parts of the world, lightning events are measured and counted in order to derive maps with average lightning activity. For example, 10 lightning events have to be expected per square kilometer and year on average in some areas in Germany. Hence, around 10.000 lightning events per year occurring at a distance of less than 500 m from the fiber have to be expected for a link with a length of 1.000 km in these areas.

Typical lightning events with negative current flow exhibit peak currents of 20 kA. In less than 10% of the events, the current flows in the other direction and reaches peak values of up to 300 kA [9]. Other sources are reporting that current change rates of 100 kA/µs have to be expected on average and change rates exceeding 400 kA/µs can be observed in 1% of lightning events [10]. The Verdet constant of silica fibers reaches values of 0.53 rad / (T m) at a wavelength around 1550 nm [11]. According to Eq. (11), polarization rotation angles up to 0.1 rad can be expected for nearby lightning events with positive current. As the rise time of the current can fall below 1 µs, similar rise times have to be expected for the polarization rotation, corresponding to polarization rotation speeds of more than 100 krad/s.

Up to this point, we have considered lightning strikes in the vicinity of the cable with the optical fiber. If the fiber is installed in the ground wire of overhead electrical power transmission lines (OPGW), lightning current can also flow in these ground wires after a direct hit. In a typical cable, the fibers are contained in an aluminum tube with several layers of steel and aluminum strands wrapped around the tube. The outer layer usually consists of aluminum strands which follow a helical path. It is difficult to predict, what kind of magnetic fields will be generated around the fibers, if lightning directly hits one of the outer strands and initiates a current flow.

If all metal strands were perfectly conducting and if there was no resistance between the strands, the fibers would be protected from electric fields by an ideal Faraday cage. Hence, the magnetic fields due to the current flowing along the OPGW would be orthogonal to the fiber axis and not rotate polarization. As mentioned above, the strands of the outer layer are predominantly manufactured from aluminum which rapidly forms a poorly conducting oxide layer on its surface. In addition, the contact surfaces of the individual wires are small, so it appears plausible that conductive coupling between the strands is rather small. There is still inductive and capacitive coupling, but the latter two require some propagation distance before the current is distributed across all strands of the outer layer. In the transition length, at least a part of the current will flow helically around the fiber, just as in a coil, producing a magnetic field parallel to the fiber. It is hard to quantify the magnitude of this effect since it depends on the exact circumstances, such as the OPGW geometry, materials, aging, exact location where the discharge hits and its temporal structure.

Two more effects have to be considered. Current will flow on both sides of the spot where the lightning bolt hits the cable, but in opposite directions. On one side of the spot, the current will flow parallel to the propagation direction of the optical wave and anti-parallel on the other side. Hence, polarization rotations generated by the Faraday effect due to helical current components on one side of the spot can cancel the ones on the other side depending on symmetry. The time evolution of current flows in the OPGW is dictated by the characteristics of the electrical transmission line. In general, rise times of the current inside the wire will be larger than the rise time of the current in the lightning discharge arc due to the inductance of the line.

With all these effects acting together, it is rather difficult to estimate the magnitude and rise time of polarization rotations induced by direct hits of OPGW. Rise times will probably reach a few µs, which is longer than the 1 µs expected for lightning strikes in the vicinity of the cable. The magnitude depends strongly on the deviation from symmetry. Differences in the current flow on one side of the spot where the lightning bolt hits compared to the other side will result in remaining polarization rotations. Moreover, the fiber inside the tube probably does not follow a straight path. Depending on the cable design and manufacturing process, the path will also be helical. As a consequence, electrical currents flowing parallel to the axis of the cable result in magnetic field components parallel to the propagation of the optical wave. As the alignment between the helical paths of the aluminum strand and the fiber will probably be different on both sides of the spot where the lightning hits, remaining polarization rotations have to be expected.

Even small asymmetries potentially result in considerable polarization rotation magnitudes due to the small spacing between the fiber and the strong currents, which generate strong magnetic fields at the location of the optical waveguides. In an experiment with an OPGW section with a length of 200 m and a peak current of 16 kA flowing through the cable, polarization rotations with magnitudes up to 35 degrees and rise times of 15 µs have been observed [12]. The current was flowing from one end of the cable to the other, so the cancelling effect with currents flowing in opposite directions did not occur. If the lightning hits the wire at a location between the grounded posts, there will be some cancelling due to currents flowing in both directions. The remaining effect can potentially still lead to considerable polarization rotations.

Note, that lightning strikes to OPGW are no rare phenomena. For central Europe the frequency of occurrence has been estimated to about 30 hits per 100 km of OPGW and year, and can be considerably higher approaching the equator. It is not unlikely that the polarization rotations induced by direct hits achieve similar or even higher magnitudes than the ones resulting from lightning current in the vicinity of the cable. Hence, both types of lightning events should be considered when defining response time requirements for receivers.

2.2 Sensitivity to phase fluctuations due to coherent detection

In a system with PolMUX transmission, optical polarization control and direct detection, polarization excursions of 0.1 rad would probably result in a tolerable penalty, even if the polarization controller was not able to follow such fast polarization transients. However, additional effects have to be considered in case of local oscillator based coherent detection. The availability of the phase information of the optical signal in the electrical domain enables to compensate linear effects such as chromatic dispersion or polarization mode dispersion by digital signal processing. Many transponders for 100 Gbit/s signals are able to tolerate differential group delay (DGD) values of more than 100 ps according to their specification.

The interplay between fast polarization rotations and other linear or nonlinear effects such as PMD, CD or cross polarization phase modulation (XPolPM) can have an impact on signal phase. Consequently, the MIMO equalizer is not the only module in the DSP chain which can be affected by fast polarization rotations. As an example, we analyze the potential impact of polarization rotations in combination with PMD on the carrier frequency and phase recovery.

The Faraday effect induces circular birefringence, resulting in different propagation constants of the right hand and the left hand circular polarizations. The deviating propagation constants of the two orthogonal polarization states lead to an alteration of the slope in case of linear polarizations, corresponding to a rotation of the electrical field vector in a plane perpendicular to the propagation direction of the optical wave. In the general case, the polarization state is rotated around the s3 axis in Stokes space. If the fiber section with the polarization rotation is followed by a section with linear birefringence, the excitation of the fast axis and the slow axis potentially changes.

The transmission matrix of a linear birefringent element in the Jones representation can be written in the following form:

TDGD=[exp(jφ2)00exp(jφ2)],
where φ denotes the phase rotation experienced by the signals propagating in the slow and the fast principal axis, respectively. The phase rotation depends on the differential group delay Δτ of the birefringent element and the angular frequency ω of the optical signal:
φ=ωΔτ.
For example, with optical signals at a wavelength of 1550 nm, corresponding to a frequency of 193.4 THz and a birefringent element with a DGD of 100 ps, the phase difference of signal components propagating in the fast principal axis and the slow one has accumulated to 122 krad at the output of the element.

A rotation of the polarization state at the input of the birefringent element from linear horizontal to linear vertical, i. e. by 90 degree or π/2 rad, results in a phase shift with the magnitude φ of the signal components propagating in the principal axes. One component makes a transition from the fast to the slow axis and the other vice versa. If the polarization rotation occurs within 1 µs, which corresponds to the typical transition time of the leading edge of current flows in lightning events, the phase of the optical signal components changes with a rate of 122 krad / 1 µs = 120 Grad/s. This results in a temporal change of the optical signal frequency by 120 Grad/s / (2 π) = 19.1 GHz. Even if the magnitude of the polarization rotation does not reach π/2 rad but only 0.1 rad, as in the case of lightning events with positive current, the temporal frequency changes can still exceed 1.2 GHz.

In a typical DSP implementation, the butterfly filter structure used for MIMO equalization is followed by a carrier frequency estimation (CFE) stage. If the MIMO equalizer was able to respond immediately to the polarization rotation, it would also compensate the phase changes which result in the frequency shifts of the signal components. Without a sufficiently fast response of the MIMO equalizer, the signal components with the temporal frequency shifts enter the following DSP stage, the carrier frequency estimation, which may not be able to tolerate temporal fluctuations of the optical carrier frequency exceeding 1.2 GHz.

Another critical aspect can arise from the opposite signs of the frequency shifts of the two orthogonal polarization components. Both components experience a frequency shift with the same magnitude, but due to the opposite signs, a joint carrier frequency recovery may average out the frequency shifts. If the frequency shifts are not corrected by the CFE, the following carrier phase estimation (CPE) will not be able to tolerate them. As the DSP typically uses block processing, a temporal failure of the CFE or the CPE probably results in at least one block full of symbol errors. It is rather unlikely that the forward error correction (FEC) decoder is capable of correcting all these errors.

Without a sufficiently fast response of the butterfly filter structure, the receiver will lose track in case of polarization rotations with large magnitudes, i. e. rotation angles approaching π/4 rad or more, due to strong crosstalk between polarization channels. This crosstalk will result in many symbol errors regardless of the response of the following DSP stages. Fast polarization rotations with small magnitudes induce weak crosstalk. Even without any response of the butterfly filter, such small amounts of crosstalk could be tolerable by assigning some optical signal to noise ratio (OSNR) margin. However, a fast and appropriate response of the butterfly filter is still necessary in order to avoid failure of following DSP stages due to frequency shifts induced by fast polarization rotations in combination with PMD.

The configuration with a polarization rotation at the input of a birefringent element was chosen to illustrate the mechanism which converts polarization rotations into frequency shifts of optical signal components. The description is not meant as a statement that this configuration is the most challenging one for local oscillator based coherent receivers with DSP. On the contrary, a well-adapted MIMO equalizer will avoid such frequency shifts in this configuration, even without any adaptation of the coefficients, as explained below.

The goal of the adaptation of the coefficients of the MIMO equalizer is to approximate the inverse PMD transfer function of the optical fiber link in front of the receiver. If the optical fiber link contains a single birefringent element with a given DGD, the coefficients of the MIMO equalizer should converge to values which correspond to a transfer function of a birefringent element with the same DGD value as the one in the link but an orientation which is rotated by 90 degrees. Due to this rotation, signal components propagating through the fast principal axis of the birefringent element in the fiber will propagate through the slow principal axis in the birefringent element modeled by the MIMO equalizer and vice versa. In the ideal case, the two birefringent elements completely compensate each other. A polarization rotation in front of the first birefringent element does not alter the frequency of signal components at the output of the second birefringent element, as the net first order PMD of the cascade is zero.

So polarization rotations at the input or at the output of the cascade of the two birefringent elements do not result in frequency shifts of signal components, but polarization rotations between the two birefringent elements can induce frequency shifts. Without a response of the MIMO equalizer, polarization rotations after the output of the birefringent element in the fiber change the alignment of the cascade of two birefringent elements. The phase difference after propagation through the second birefringent element does no longer reverse the phase difference after propagation through the first birefringent element, which leads to a frequency shift. Similar frequency shifts can also occur, if the polarization rotations are located along the fiber sections which contribute first order PMD to the first birefringent element.

So far, the analysis was focusing on worst case scenarios. The amount of phase shift induced by birefringent elements during polarization rotations depends on the location of the polarization rotation relative to the birefringent elements and polarization states at their input at the beginning of the lightning event. Moreover, even if the transponders are specified to be able to tolerate 100 ps of DGD, the actually occurring first order PMD in the transmission fiber will usually be smaller. This reduces the probability that polarization transients induced by lightning events will result in post FEC errors. However, the prospect of several hundred lightning events with positive current per year which can induce polarization rotations with magnitudes around 0.1 rad on time scales of 1 µs in long haul links emphasizes the importance of the capability of transponders to tolerate such events. This is especially relevant for optical fibers which are installed in ground wires of overhead electrical power transmission lines, because such fibers are much more exposed to lightning events.

2.3 Definition of response time requirements

Special care should be taken when interpreting the speed of polarization rotations or defining the tolerance of transponders. In this work, the term polarization rotation refers to the change of the direction of the electrical field vector in the plane perpendicular to the direction of wave propagation. It is also possible to consider the angle between two polarization states in Stokes space or on the Poincare sphere. The angle on the Poincare sphere is larger than the rotation angle of the electrical field vector by a factor of 2. Moreover, a variation of the phase shift between two orthogonal linear polarization components also results in a rotation of the state of polarization (SOP) in Stokes space as well as on the Poincare sphere.

A rotation of a linear polarization state at the input of a linear birefringent element can result in several hundred or thousand rotations around the s1 axis in Stokes space at the output of the element. For example, the rotation of the electrical field vector at the input of the element by an angle of π/2 rad, corresponding to a SOP rotation in Stokes space of π rad, is transformed into SOP rotations in Stokes space of Δτ * ω rad at the output, where Δτ denotes the DGD in ps and ω the angular frequency of the optical carrier in THz. If the change of the direction of the electrical field vector occurs within 10 µs, it rotates at the input with a speed of π/2 * 100 krad/s, corresponding to π * 100 krad/s in Stokes space. This polarization rotation can result in SOP rotations in Stokes space with a speed of more than 12 Grad/s at the output of a birefringent element with a DGD of 100 ps,

Fortunately this does not imply that the butterfly equalizer in the receiver has to be able to track polarization rotations in the Grad/s range. If the equalizer was well adapted before the polarization rotation, its filter settings correspond to a birefringent element with the same DGD value but an orientation of the fast and slow principal axis which is rotated by 90 degrees compared to the birefringent element in the link. During the polarization rotation in front of the birefringent element in the fiber, the filter coefficients modelling the birefringent element in the receiver can be kept constant – as shown above. Only the filter coefficients modelling a polarization rotation at the output of the birefringent element in the receiver have to be adapted. Consequently, we recommend that tolerances of transponders should be specified for rotation speeds of the electrical field vector and not SOP rotation speeds in Stokes space at the output of a link. On the other hand, if one wants to measure the time evolution of SOPs at the output of a link to determine the speed of polarization fluctuations, the polarimeter has to be able to track speeds beyond 1 Grad/s, as accumulated link DGD values of a few ps have to be expected in long haul links.

Current transponder generations with bit rates up to 100 Gbit/s use QPSK modulation for transmission of two bits per symbol. Higher order modulation formats such as 16 QAM will be used in future transponder generations in order to increase bit rate and spectral density. Using more constellation points and increasing the number of bits per symbol increase the challenges of MIMO equalization. The realization of sufficiently fast MIMO equalizers for these higher order modulation formats, which tend to be less tolerant towards signal distortion, will be even more difficult than the ones for QPSK.

The theoretical study has so far focused on polarization rotations induced by the Faraday effect and potential phase fluctuations of signal components due to first order PMD. The high peak currents caused by lightning events can result in additional effects such as mechanical vibrations or temperature changes. These effects can result in additional polarization rotations or phase fluctuations which may aggravate the impact of the lightning event. Together with the polarization rotations induced by the Faraday effects, these effects result in demanding response time requirements on receivers.

3. Experimental investigations

The theoretical analysis has revealed that lightning events can result in alterations of transmitted optical signals which are potentially challenging for local oscillator based coherent receivers with digital signal processing. As it is rather difficult to investigate the dynamic response of DSP algorithms by off-line processing, real-time implementations have been chosen to study the potential impact of lightning events. The main purpose of the experiments was to check, whether fast polarization rotations on the time scales of lightning events pose threats to the error free operation of transponders or if response times of typical implementations are sufficiently fast, enabling them to tolerate such events.

3.1 Experimental set-ups

Two different experimental set-ups were used for measuring the influence of fast polarization rotations due to a lightning stroke. Figure 3 shows a block diagram of the set-up which was used to study the impact on continuous wave (CW) signals and Fig. 4 the set-up used for the investigation of the impact on the transmission performance of prototype 100G transponders.

 

Fig. 3 Block diagram of the experimental set-up used for measuring the influence of lightning stroke currents on a continuous wave (CW) signal generated by an external cavity laser (ECL) propagating in standard single mode fiber (SSMF).

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Fig. 4 Block diagram of the experimental set-up used for measuring the influence of lightning stroke currents on modulated signals propagating through an element with differential group delay (DGD). This set-up also contains polarization maintaining fibers (PMF), variable optical attenuators (VOA), erbium doped fiber amplifiers (EDFA), optical bandpass filters (OBPF), an optical spectrum analyzer (OSA), and an optical power meter (OPM).

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For analyzing the fast polarization rotations with a CW signal, such a signal is generated using an external cavity laser and it is transmitted to the high current generator in a fiber. After passing the high current generator the signal is split with a 3 dB coupler to measure the polarization state using a fast polarimeter on the one hand and to detect the signal using a coherent receiver consisting of a polarization diverse coherent optical frontend in combination with a high speed digital storage oscilloscope on the other hand. Several hundred meters of SSMF are used to connect all components.

Modulated signals are generated using prototype coherent 100G transponders. One transponder at a time is connected to a polarization controller to either set or to scramble the state of the polarization of the optical wave. The high current generator is connected to the polarization controller using SSMF on the input and connected to a DGD element at the output. The set-up of the DGD element is shown in Fig. 4: the optical wave is split into two components with orthogonal polarizations by a polarization beam splitter (PBS). While one arm of the PBS is connected to a second PBS using a polarization maintaining fiber (PMF), the second arm contains a variable delay introduced by a tunable optical delay line. The second PBS is used to recombine the two signal components with orthogonal polarization states. The DGD element is capable of generating first order PMD in a range from ~5 ps to ~90 ps. It is followed by a 3 dB coupler. One output of this coupler is connected to a coherent receiver consisting of a coherent optical frontend and a digital storage oscilloscope which is triggered to record the signal during the polarization transient. The second output is connected to a noise loading set-up, shown in Fig. 4. The EDFA following the coupler with the OSA attached to it is a part of the noise-loading set-up, but it has been verified that its contribution to the overall OSNR is negligible. The output of the noise loading is connected to the receiver of the prototype transponder to analyze the received signal.

The structure of the high current generator is shown in Fig. 5(a). In order to generate a single current impulse with high peak current, a capacitor is charged and afterwards rapidly discharged over a shorting bar. The time evolution of the discharge current of this generator is shown in Fig. 5(b)). It can be read from the figure that the peak current of this system reaches 31 kA, while the rise time from 10% of the peak current to 90% of the peak current is 4.05 µs. An SSMF fiber section is wrapped around the shorting bar multiple times. Images of the generator are shown in Fig. 6.

 

Fig. 5 a) Scheme of the high current generator. b) Time evolution of the discharge current of the high current generator. The peak current is 31 kA, the rise time from 10% to 90% of the peak current is 4.05 µs and the time from 10% peak power to 50% peak power is 20.7 µs.

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Fig. 6 Images of the high current generator used for the experiments.

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As stated in the preceding section, the peak current of lightning strokes with positive current flows can reach 300 kA. To compensate the lower peak current of the high current generator the fiber is wrapped around the shorting bar 30 times to increase the Faraday effect. This increases the angle of the polarization rotation approx. by a factor of 60 compared to the straight line fiber configuration shown in Fig. 1. A factor of 10 was used to compensate the smaller peak current. The remaining factor was used to compensate the slower rise time and partial field cancelling due to currents flowing in opposite directions in the generator. The reason for the longer rise time of the current in the high current generator compared to average lightning events is, that it was designed to test the impact of impulse currents on nonlinear resistive components in electrical power distribution networks. Before the lightning current reaches the equipment, it is transmitted through an electrical transmission line. This transmission acts like a low pass filter and increases the rise time. Therefore, the high current generator emulates the time evolution after transmission and has a larger rise time than the current in the discharge arc of the lightning event.

Additionally, due to the design of the generator, the magnetic field intensity at the fiber is partly (~15%) cancelled by magnetic fields pointing in opposite directions. With the compensation of the smaller peak current, the reduced magnetic field and the larger rise time of the high current generator by multiple windings of the fiber, the polarization rotation rate corresponds approx. to the one with a peak current of 300 kA and a rise time slightly below 1 µs.

The course of the experiments was as follows. When analyzing CW signals, the signal source is turned on and an event of high current is triggered. The polarization time evolution is recorded by the fast polarimeter and the signal is also captured by the coherent receiver for offline processing.

In the case of modulated signals, additional care has to be taken: the prototype transponders feature a full DSP stack including FEC. The goal of the experiments is to check, whether post-FEC errors occur. The question arises how close the transponder has to be operated to the FEC-threshold. To address this question, the noise loading set-up was adjusted to achieve different OSNR values and to find the FEC-threshold. The actual OSNR of the FEC-threshold depends on several other parameters of the experiment, namely the operation mode of the polarization controller (scrambling or constant) and the additional PMD of the DGD element. Once the FEC-threshold was found, the OSNR was increased slightly to introduce some margin with respect to the FEC-threshold and to obtain error-free operation without fast polarization rotations.

After an event of high current was triggered, the signal was recorded using the coherent receiver for offline processing and the transponder log was checked for post-FEC errors. The experiment was repeated several times with different OSNR margins.

3.2 Results

The results from the post-processing of data recorded by the coherent receiver with the CW signal are shown in Fig. 7. Subfigures a) and b) show the change of the polarization state due to an event of high current. Figure 7(a) shows the evolution of the normalized Stokes parameters over time. Noticeable changes in these parameters are visible starting at ~5 µs. These changes in the polarization state show the same time constants as the time evolution of the discharging current of the high current generator (see Fig. 5(b)). Figure 7(b) shows the change rate of the polarization angle dχ/dt in krad/s where χ denotes the rotation angle of the electrical field vector with a maximum rotation speed of 270 krad/s. Figure 7(c) combines the information from Figs. 7(a) and 7(b) and displays them on the Poincaré sphere. The polarization state is rotated around the s3-axis. The accumulated change of the angle 2χ is 166.05°. These results show that an event of high current induces a rotation of the polarization of the optical wave.

 

Fig. 7 Analysis of polarization rotations of a CW signal due to a high current event; the signal was recorded using a coherent receiver; a) shows the time evolution of the normalized Stokes parameters, b) shows the variation of the polarization angle χ and c) shows the Poincaré presentation of the evolution of the Stokes parameters over time. The accumulated change of the polarization angle 2χ on the Poincaré sphere is 166.05°.

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Measurements with modulated signals were carried out with two different 100G transponder prototypes, one equipped with hard decision FEC (Prototype No. 1) and the other with soft decision FEC (Prototype No. 2). Table 1 shows the results with different DGD values. For each DGD value, four high current events were measured with the polarization scrambler turned on. Pre-FEC BER values recorded before the high current event are listed in the third column. The last column in Table 1 shows the relative frequency of occurrence of post FEC errors. A value of 1 corresponds to the case with post FEC errors during every high current event, for a value of 0.5, only half of the high current events have resulted in post FEC errors. If an individual high current event has resulted in post FEC errors, several thousand errored symbols have been recorded per event.

Tables Icon

Table 1. Relative frequency of post-FEC errors

4. Summary and conclusions

The potential impact of fast polarization rotations caused by lightning events on the error free operation of local oscillator based coherent optical receivers with digital signal processing has been analyzed theoretically and experimentally. Theoretical considerations have revealed that lightning currents can induce polarization rotations with magnitudes up to 0.1 rad on time scales of 1 µs due to the Faraday effect. In combination with PMD, the polarization rotations can result in temporal frequency changes of signal components. If the polarization changes are not compensated by the butterfly filter structure used for MIMO equalization in the DSP, it is rather unlikely that the carrier frequency and phase estimation will be able to tolerate the resulting frequency fluctuations in all cases, which potentially leads to post FEC errors.

Experimental investigations were carried out in order to verify the predictions from the theoretical analysis and to test the capability of real time signal processing to tolerate fast polarization transients and resulting effects. A high current pulse generator was used to induce polarization rotations by the Faraday effect in an optical signal travelling through a fiber. The induced polarization changes were analyzed with a CW signal and a fast polarimeter. After replacing the CW signal by the output signal of prototype transponders, the same polarization rotations were applied to modulated signals. Post FEC error bursts resulting from the polarization transients have been observed when detecting the signal with receivers of transponder prototypes. The investigations show that polarization rotations induced by lightning events are potentially challenging for local oscillator based coherent receivers with digital signal processing and that the response times of current implementations may be insufficient to tolerate events occurring in the field.

References and links

1. N. E. Hecker, E. Gottwald, K. Kotten, C.-J. Weiske, A. Schöpflin, P. M. Krummrich, and C. Glingener, “Automated polarization control demonstrated in a 1.28 Tbit/s (16x2x40 Gbit/s) polarization multiplexed DWDM field trial,” in 27th European Conference on Optical Communication (ECOC, 2001), paper Mo.L.3. [CrossRef]  

2. J. Wuttke, P. M. Krummrich, and J. Rösch, “Polarization oscillations in aerial fiber caused by wind and power-line current,” IEEE Photonics Technol. Lett. 15(6), 882–884 (2003). [CrossRef]  

3. P. M. Krummrich and K. Kotten, “Extremely fast (microsecond timescale) polarization changes in high speed long haul WDM transmission systems,” in Conference on Optical Fiber Communication (OFC, 2004), paper FI3.

4. P. M. Krummrich, E.-D. Schmidt, W. Weiershausen, and A. Mattheus, “Field trial results on statistics of fast polarization changes in long haul WDM transmission systems,“ in Conference on Optical Fiber Communication (OFC, 2005), paper OThT6. [CrossRef]  

5. M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photonics Technol. Lett. 16(2), 674–676 (2004). [CrossRef]  

6. D. S. Ly-Gagnon, K. Katoh, and K. Kikuchi, “Unrepeated 210-km transmission with coherent detection and digital signal processing of 20-Gb/s QPSK signal,” in Conference on Optical Fiber Communication (OFC, 2005), paper OTuL4. [CrossRef]  

7. M. Kurono, M. Kuribara, and K. Isawa, “Field measurements and a study of transient state of polarization produced in OPGW by lightning,” Electr. Eng. Jpn. 128(4), 55–64 (1999). [CrossRef]  

8. S. M. Pietralunga, J. Colombelli, A. Fellegara, and M. Martinelli, “Fast polarization effects in optical aerial cables caused by lightning and impulse current,” IEEE Photonics Technol. Lett. 16(11), 2583–2585 (2004). [CrossRef]  

9. V. A. Rakov and M. A. Uman, Lightning: Physics and Effects (Cambridge University Press, 2007), Chap. 5.

10. W. R. Gamerota, J. O. Elismé, M. A. Uman, and V. A. Rakov, “Current waveforms for lightning simulation,” IEEE Trans. Electromagn. Compat. 54(4), 880–888 (2012). [CrossRef]  

11. J. L. Cruz, M. V. Andres, and M. A. Hernandez, “Faraday effect in standard optical fibers: dispersion of the effective Verdet constant,” Appl. Opt. 35(6), 922–927 (1996). [CrossRef]   [PubMed]  

12. M. Kurono, K. Isawa, and M. Kuribara, “Transient state of polarization on optical ground wire caused by lightning and impulse current,” Proc. SPIE 2873, 242–245 (1996). [CrossRef]  

References

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  1. N. E. Hecker, E. Gottwald, K. Kotten, C.-J. Weiske, A. Schöpflin, P. M. Krummrich, and C. Glingener, “Automated polarization control demonstrated in a 1.28 Tbit/s (16x2x40 Gbit/s) polarization multiplexed DWDM field trial,” in 27th European Conference on Optical Communication (ECOC, 2001), paper Mo.L.3.
    [Crossref]
  2. J. Wuttke, P. M. Krummrich, and J. Rösch, “Polarization oscillations in aerial fiber caused by wind and power-line current,” IEEE Photonics Technol. Lett. 15(6), 882–884 (2003).
    [Crossref]
  3. P. M. Krummrich and K. Kotten, “Extremely fast (microsecond timescale) polarization changes in high speed long haul WDM transmission systems,” in Conference on Optical Fiber Communication (OFC, 2004), paper FI3.
  4. P. M. Krummrich, E.-D. Schmidt, W. Weiershausen, and A. Mattheus, “Field trial results on statistics of fast polarization changes in long haul WDM transmission systems,“ in Conference on Optical Fiber Communication (OFC, 2005), paper OThT6.
    [Crossref]
  5. M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photonics Technol. Lett. 16(2), 674–676 (2004).
    [Crossref]
  6. D. S. Ly-Gagnon, K. Katoh, and K. Kikuchi, “Unrepeated 210-km transmission with coherent detection and digital signal processing of 20-Gb/s QPSK signal,” in Conference on Optical Fiber Communication (OFC, 2005), paper OTuL4.
    [Crossref]
  7. M. Kurono, M. Kuribara, and K. Isawa, “Field measurements and a study of transient state of polarization produced in OPGW by lightning,” Electr. Eng. Jpn. 128(4), 55–64 (1999).
    [Crossref]
  8. S. M. Pietralunga, J. Colombelli, A. Fellegara, and M. Martinelli, “Fast polarization effects in optical aerial cables caused by lightning and impulse current,” IEEE Photonics Technol. Lett. 16(11), 2583–2585 (2004).
    [Crossref]
  9. V. A. Rakov and M. A. Uman, Lightning: Physics and Effects (Cambridge University Press, 2007), Chap. 5.
  10. W. R. Gamerota, J. O. Elismé, M. A. Uman, and V. A. Rakov, “Current waveforms for lightning simulation,” IEEE Trans. Electromagn. Compat. 54(4), 880–888 (2012).
    [Crossref]
  11. J. L. Cruz, M. V. Andres, and M. A. Hernandez, “Faraday effect in standard optical fibers: dispersion of the effective Verdet constant,” Appl. Opt. 35(6), 922–927 (1996).
    [Crossref] [PubMed]
  12. M. Kurono, K. Isawa, and M. Kuribara, “Transient state of polarization on optical ground wire caused by lightning and impulse current,” Proc. SPIE 2873, 242–245 (1996).
    [Crossref]

2012 (1)

W. R. Gamerota, J. O. Elismé, M. A. Uman, and V. A. Rakov, “Current waveforms for lightning simulation,” IEEE Trans. Electromagn. Compat. 54(4), 880–888 (2012).
[Crossref]

2004 (2)

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photonics Technol. Lett. 16(2), 674–676 (2004).
[Crossref]

S. M. Pietralunga, J. Colombelli, A. Fellegara, and M. Martinelli, “Fast polarization effects in optical aerial cables caused by lightning and impulse current,” IEEE Photonics Technol. Lett. 16(11), 2583–2585 (2004).
[Crossref]

2003 (1)

J. Wuttke, P. M. Krummrich, and J. Rösch, “Polarization oscillations in aerial fiber caused by wind and power-line current,” IEEE Photonics Technol. Lett. 15(6), 882–884 (2003).
[Crossref]

1999 (1)

M. Kurono, M. Kuribara, and K. Isawa, “Field measurements and a study of transient state of polarization produced in OPGW by lightning,” Electr. Eng. Jpn. 128(4), 55–64 (1999).
[Crossref]

1996 (2)

J. L. Cruz, M. V. Andres, and M. A. Hernandez, “Faraday effect in standard optical fibers: dispersion of the effective Verdet constant,” Appl. Opt. 35(6), 922–927 (1996).
[Crossref] [PubMed]

M. Kurono, K. Isawa, and M. Kuribara, “Transient state of polarization on optical ground wire caused by lightning and impulse current,” Proc. SPIE 2873, 242–245 (1996).
[Crossref]

Andres, M. V.

Colombelli, J.

S. M. Pietralunga, J. Colombelli, A. Fellegara, and M. Martinelli, “Fast polarization effects in optical aerial cables caused by lightning and impulse current,” IEEE Photonics Technol. Lett. 16(11), 2583–2585 (2004).
[Crossref]

Cruz, J. L.

Elismé, J. O.

W. R. Gamerota, J. O. Elismé, M. A. Uman, and V. A. Rakov, “Current waveforms for lightning simulation,” IEEE Trans. Electromagn. Compat. 54(4), 880–888 (2012).
[Crossref]

Fellegara, A.

S. M. Pietralunga, J. Colombelli, A. Fellegara, and M. Martinelli, “Fast polarization effects in optical aerial cables caused by lightning and impulse current,” IEEE Photonics Technol. Lett. 16(11), 2583–2585 (2004).
[Crossref]

Gamerota, W. R.

W. R. Gamerota, J. O. Elismé, M. A. Uman, and V. A. Rakov, “Current waveforms for lightning simulation,” IEEE Trans. Electromagn. Compat. 54(4), 880–888 (2012).
[Crossref]

Hernandez, M. A.

Isawa, K.

M. Kurono, M. Kuribara, and K. Isawa, “Field measurements and a study of transient state of polarization produced in OPGW by lightning,” Electr. Eng. Jpn. 128(4), 55–64 (1999).
[Crossref]

M. Kurono, K. Isawa, and M. Kuribara, “Transient state of polarization on optical ground wire caused by lightning and impulse current,” Proc. SPIE 2873, 242–245 (1996).
[Crossref]

Krummrich, P. M.

J. Wuttke, P. M. Krummrich, and J. Rösch, “Polarization oscillations in aerial fiber caused by wind and power-line current,” IEEE Photonics Technol. Lett. 15(6), 882–884 (2003).
[Crossref]

Kuribara, M.

M. Kurono, M. Kuribara, and K. Isawa, “Field measurements and a study of transient state of polarization produced in OPGW by lightning,” Electr. Eng. Jpn. 128(4), 55–64 (1999).
[Crossref]

M. Kurono, K. Isawa, and M. Kuribara, “Transient state of polarization on optical ground wire caused by lightning and impulse current,” Proc. SPIE 2873, 242–245 (1996).
[Crossref]

Kurono, M.

M. Kurono, M. Kuribara, and K. Isawa, “Field measurements and a study of transient state of polarization produced in OPGW by lightning,” Electr. Eng. Jpn. 128(4), 55–64 (1999).
[Crossref]

M. Kurono, K. Isawa, and M. Kuribara, “Transient state of polarization on optical ground wire caused by lightning and impulse current,” Proc. SPIE 2873, 242–245 (1996).
[Crossref]

Martinelli, M.

S. M. Pietralunga, J. Colombelli, A. Fellegara, and M. Martinelli, “Fast polarization effects in optical aerial cables caused by lightning and impulse current,” IEEE Photonics Technol. Lett. 16(11), 2583–2585 (2004).
[Crossref]

Pietralunga, S. M.

S. M. Pietralunga, J. Colombelli, A. Fellegara, and M. Martinelli, “Fast polarization effects in optical aerial cables caused by lightning and impulse current,” IEEE Photonics Technol. Lett. 16(11), 2583–2585 (2004).
[Crossref]

Rakov, V. A.

W. R. Gamerota, J. O. Elismé, M. A. Uman, and V. A. Rakov, “Current waveforms for lightning simulation,” IEEE Trans. Electromagn. Compat. 54(4), 880–888 (2012).
[Crossref]

Rösch, J.

J. Wuttke, P. M. Krummrich, and J. Rösch, “Polarization oscillations in aerial fiber caused by wind and power-line current,” IEEE Photonics Technol. Lett. 15(6), 882–884 (2003).
[Crossref]

Taylor, M. G.

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photonics Technol. Lett. 16(2), 674–676 (2004).
[Crossref]

Uman, M. A.

W. R. Gamerota, J. O. Elismé, M. A. Uman, and V. A. Rakov, “Current waveforms for lightning simulation,” IEEE Trans. Electromagn. Compat. 54(4), 880–888 (2012).
[Crossref]

Wuttke, J.

J. Wuttke, P. M. Krummrich, and J. Rösch, “Polarization oscillations in aerial fiber caused by wind and power-line current,” IEEE Photonics Technol. Lett. 15(6), 882–884 (2003).
[Crossref]

Appl. Opt. (1)

Electr. Eng. Jpn. (1)

M. Kurono, M. Kuribara, and K. Isawa, “Field measurements and a study of transient state of polarization produced in OPGW by lightning,” Electr. Eng. Jpn. 128(4), 55–64 (1999).
[Crossref]

IEEE Photonics Technol. Lett. (3)

S. M. Pietralunga, J. Colombelli, A. Fellegara, and M. Martinelli, “Fast polarization effects in optical aerial cables caused by lightning and impulse current,” IEEE Photonics Technol. Lett. 16(11), 2583–2585 (2004).
[Crossref]

J. Wuttke, P. M. Krummrich, and J. Rösch, “Polarization oscillations in aerial fiber caused by wind and power-line current,” IEEE Photonics Technol. Lett. 15(6), 882–884 (2003).
[Crossref]

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photonics Technol. Lett. 16(2), 674–676 (2004).
[Crossref]

IEEE Trans. Electromagn. Compat. (1)

W. R. Gamerota, J. O. Elismé, M. A. Uman, and V. A. Rakov, “Current waveforms for lightning simulation,” IEEE Trans. Electromagn. Compat. 54(4), 880–888 (2012).
[Crossref]

Proc. SPIE (1)

M. Kurono, K. Isawa, and M. Kuribara, “Transient state of polarization on optical ground wire caused by lightning and impulse current,” Proc. SPIE 2873, 242–245 (1996).
[Crossref]

Other (5)

N. E. Hecker, E. Gottwald, K. Kotten, C.-J. Weiske, A. Schöpflin, P. M. Krummrich, and C. Glingener, “Automated polarization control demonstrated in a 1.28 Tbit/s (16x2x40 Gbit/s) polarization multiplexed DWDM field trial,” in 27th European Conference on Optical Communication (ECOC, 2001), paper Mo.L.3.
[Crossref]

V. A. Rakov and M. A. Uman, Lightning: Physics and Effects (Cambridge University Press, 2007), Chap. 5.

D. S. Ly-Gagnon, K. Katoh, and K. Kikuchi, “Unrepeated 210-km transmission with coherent detection and digital signal processing of 20-Gb/s QPSK signal,” in Conference on Optical Fiber Communication (OFC, 2005), paper OTuL4.
[Crossref]

P. M. Krummrich and K. Kotten, “Extremely fast (microsecond timescale) polarization changes in high speed long haul WDM transmission systems,” in Conference on Optical Fiber Communication (OFC, 2004), paper FI3.

P. M. Krummrich, E.-D. Schmidt, W. Weiershausen, and A. Mattheus, “Field trial results on statistics of fast polarization changes in long haul WDM transmission systems,“ in Conference on Optical Fiber Communication (OFC, 2005), paper OThT6.
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Sketch of the configuration which is considered to calculate the impact of lightning current on optical fiber transmission.
Fig. 2
Fig. 2 Optical fiber following a segment of a circle around the lightning current.
Fig. 3
Fig. 3 Block diagram of the experimental set-up used for measuring the influence of lightning stroke currents on a continuous wave (CW) signal generated by an external cavity laser (ECL) propagating in standard single mode fiber (SSMF).
Fig. 4
Fig. 4 Block diagram of the experimental set-up used for measuring the influence of lightning stroke currents on modulated signals propagating through an element with differential group delay (DGD). This set-up also contains polarization maintaining fibers (PMF), variable optical attenuators (VOA), erbium doped fiber amplifiers (EDFA), optical bandpass filters (OBPF), an optical spectrum analyzer (OSA), and an optical power meter (OPM).
Fig. 5
Fig. 5 a) Scheme of the high current generator. b) Time evolution of the discharge current of the high current generator. The peak current is 31 kA, the rise time from 10% to 90% of the peak current is 4.05 µs and the time from 10% peak power to 50% peak power is 20.7 µs.
Fig. 6
Fig. 6 Images of the high current generator used for the experiments.
Fig. 7
Fig. 7 Analysis of polarization rotations of a CW signal due to a high current event; the signal was recorded using a coherent receiver; a) shows the time evolution of the normalized Stokes parameters, b) shows the variation of the polarization angle χ and c) shows the Poincaré presentation of the evolution of the Stokes parameters over time. The accumulated change of the polarization angle 2χ on the Poincaré sphere is 166.05°.

Tables (1)

Tables Icon

Table 1 Relative frequency of post-FEC errors

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

I= l | H |dl .
| H ( r ) |= I 2πr .
r= y 2 + z 2 .
| H ( z ) |= I 2π d 2 + z 2 ,
H z =| H |cos( α ).
cos( α )= d r = d d 2 + z 2 .
H z ( z )= dI 2π( d 2 + z 2 ) .
dθ dz =V B z
B z ( z )= μ 0 H z ( z )= μ 0 dI 2π( d 2 + z 2 ) ,
θ= V B z dz =2V 0 B z dz = V μ 0 dI π 0 1 d 2 + z 2 dz .
θ= V μ 0 I 2 .
θ S =V μ 0 H z ( z=0 ) l eff = 0 V μ 0 H z ( z )dz.
H z ( z=0 )= I 2πd .
l eff =d π 2 .
θ S =V μ 0 H z ( z=0 ) l eff =V μ 0 I 2πd d π 2 = 1 4 V μ 0 I.
l F =2πd δ 2π =dδ
θ F =V μ 0 H z ( z=0 ) l F =V μ 0 I δ 2π .
Δ z OS = c 0 n gr τ>2 l eff ,
d max < c 0 τ π n gr ,
T DGD =[ exp( j φ 2 ) 0 0 exp( j φ 2 ) ],
φ=ωΔτ.

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